
function [moments, VC, IRF]=geNCalvoPlus_2Agg(sm_m, p0, mu_c, sig_eps_a, rho_a,weight_j );
 

% Set Fixed Parameters
%**************************************************************

theta = 4;    % Elasticity of demand
psi = 0;     % One over the Frisch elasticity of labor supply
gamma = 1;   % coefficient of relative risk aversion
FlexSSL = 1/3; % Steady State labor under flexible prices
beta = 0.96^(1/12);   % Discount factor

% Parameters of the process followed by nominal aggregate demand
% log(S_t) - log(S_t-1) = mu + nu_t
% where nu_t ~ N(0,sigma_eta^2), i.i.d.
mu = 0.0028;   %% Inflation trend
sigma_eta = 0.0065; 


mu = 0.00125;   %% Inflation trend
sigma_eta = 0.0028; 

% Set sector specific parameters
%***************************************************************
% NB: Edges of the rad grid need to be extra padded in the multi-sector 
% model because the sectors have different mean rad.

NSectors = 1;
 sm = sm_m;
 sm

sigma_eps     = [  sig_eps_a]';
alphaCalvo    = [  1-p0 ]';
  % pa           = [p_a    p_a ]';
    rho           = [   rho_a ]';
SectorWeights = [ 1  ]';

SectorWeights = SectorWeights/(sum(SectorWeights));

rad_shift =0.01;%0.015
slope = 9; levelshift = 2;
agridsize =70;%40
%%rpgridsize = 3500; %2000;
rpgridsize =1000;%300
radgridsize =150;%25

% 
if abs(sum(SectorWeights)-1)> 10^(-10), error('SectorWeights do not sum to one!'), end
% Maximum number of iterations on G
MaxItOnG = 60;
Ssize = agridsize*rpgridsize*radgridsize;

% Solve for the flexible price steady state 
%****************************************************************

par1 = sm*(theta-1)/(theta-sm*(theta-1));
FlexSSC = FlexSSL*par1^(sm/(1-sm))*(1+par1)^(-1/(1-sm));
FlexSSM = par1*FlexSSC;
FlexSSY = FlexSSC + FlexSSM;

omega = (theta-1)/theta*(1-sm)*(1+par1)*FlexSSL^(-psi-1)*FlexSSC^(1-gamma); % Level parameter on disutility of labor
omega2 = omega*(FlexSSL)^psi; % Marginal disutility of changing prices


K  = [mu_c  ]'; 

K2 = K/4000;
K = K*FlexSSY;
K2 = K2*FlexSSY;

FlexSSY = log(FlexSSY);
FlexSSL = log(FlexSSL);
FlexSSC = log(FlexSSC);
if sm > 0
    FlexSSM = log(FlexSSM);
end

% Print Out Parameters
%****************************************************************

fprintf('\n')
fprintf('theta:    %5.5f\n',theta)
fprintf('psi:      %5.5f\n',psi)
fprintf('gamma:    %5.5f\n',gamma)
fprintf('sm:       %5.5f\n',sm)
fprintf('\n')
fprintf('Size of State Space: %10.0f\n\n',Ssize)

fprintf('\n')
fprintf('K:\n')
for ii = 1:NSectors
    fprintf('   %5.4f ',K(ii)/exp(FlexSSY))
end
fprintf('\n')
fprintf('rho:\n')
for ii = 1:NSectors
    fprintf('   %5.4f ',rho(ii))
end
fprintf('\n')
fprintf('sigma_eps:\n')
for ii = 1:NSectors
    fprintf('   %5.4f ',sigma_eps(ii))
end
fprintf('\n\n')

% Set gridsizes and grid max and min
%****************************************************************

MaxUncondVar = max(((sigma_eps.^2)./(1-rho.^2)).^(1/2));
MinUncondVar = min(((sigma_eps.^2)./(1-rho.^2)).^(1/2));
MinUncondVar = max(MinUncondVar,sigma_eta);

trunc_eps = 2.5;
amax = trunc_eps*MaxUncondVar;
amin = -trunc_eps*MaxUncondVar;
ainc = (amax-amin)/(agridsize-1) - mod((amax-amin)/(agridsize-1),10^(-5));
amin = amin - mod(amin,10^(-5));
amax = amin + (agridsize-1)*ainc;

% fprintf('Gridpoints for "a" off of which the least volatile sector is simulated:\n')
% fprintf('2*trunc_eps*MinUncondVar/ainc = %5.3f\n\n',...
%     2*trunc_eps*MinUncondVar/ainc)
% if 2*trunc_eps*MinUncondVar/ainc < 20
%     error('2*trunc_eps*MinUncondVar/ainc < 20: Results unreliable!',...
%         2*trunc_eps*MinUncondVar/ainc) %#ok<CTPCT>
% end

% rp denotes the real price
% np denotes the nominal price
% The rp grid is a grid for the log of the real price
pimult = 250; % Determines sensitivity of pigrid to mu
rpmax = -amin*(1+pimult*abs(mu));
rpmin = -amax*(1+pimult*abs(mu));
if rpmax < 0.15
    rpmax = 0.15;
    rpmin = -0.15;
end
% %ajout ERwan 18 avril 2017
%  rpmax = 0.3;
%  rpmin = -0.3;

rpinc = (rpmax-rpmin)/(rpgridsize-1) - mod((rpmax-rpmin)/(rpgridsize-1),10^(-5));
rpmin = rpmin - mod(rpmin,10^(-5));
rpmax = rpmin + (rpgridsize-1)*rpinc;

if rpinc > 0.0075
    error('rpinc > 0.0075: Results unreliable')
end

radmin = FlexSSC - radgridsize/2*rpinc + rad_shift;

% Create the real price and idiosyncratic productivity vectors
%**************************************************************

a = amin:ainc:amax; a = a';

rp = zeros(rpgridsize,1);
rp(1) = rpmin;
for ii = 2:rpgridsize
    rp(ii) = rp(ii-1) + rpinc;
end

rad = zeros(radgridsize,1);
rad(1) = radmin;
for ii = 2:radgridsize
    rad(ii) = rad(ii-1) + rpinc;
end

% Create Probability Distribution for the idiosyncratic shock
%**************************************************************
% Proba is a matrix that gives transition probabilities of going
% from state a to state a', i.e. Proba(i,j) = Prob(a' = j | a = i)
% 
% The procedure of Tauchen (1986) is used to approximate the 
% AR(1) process for log(A_it)

for ii = 1:NSectors
    Proba(ii).Proba = CreateProba(rho(ii),sigma_eps(ii),a);
end

% Create probability distribution for nominal aggregate demand
%***************************************************************

ProbNgr = CreateProbNgr(mu,sigma_eta,rad);

% Guess a matrix G which gives the log inflation rate given S_t/P_t-1
%**************************************************************

G = zeros(radgridsize,1);
%G = (rp(2)-rp(1))*ones(radgridsize,1);
G(1,1) = -(radgridsize/(2*slope)-mod(radgridsize/(2*slope),1))*(rp(2)-rp(1)) ...
    + levelshift*(rp(2)-rp(1));
for ii = 2:radgridsize
    if mod(ii,slope) == 0
        G(ii,1) = G(ii-1,1) + rp(2) - rp(1);
    else
        G(ii,1) = G(ii-1,1);
    end
end

% Calculate the profit function
%**************************************************************

par1 = psi+1;
par2 = gamma;
par3 = exp(FlexSSC)/exp(FlexSSY);
par4 = exp(FlexSSM)/exp(FlexSSY) - sm;
par5 = 1-sm;

a3d = repmat(a,[1 rpgridsize radgridsize]);

rp3d = repmat(rp,[1 agridsize radgridsize]);
rp3d = permute(rp3d, [2 1 3]);

rad3d = repmat(rad,[1 agridsize rpgridsize]);
rad3d = permute(rad3d,[2 3 1]);

if sm > 0
    l3d = FlexSSL + (par3+par2*par4)/(par5-par1*par4)*(rad3d-FlexSSC);
    m3d = FlexSSM + par1*(l3d - FlexSSL) + par2*(rad3d-FlexSSC);
else
    l3d = FlexSSL + (rad3d-FlexSSC);
    m3d = 0*rad3d;
end

rPi3d = exp(rad3d + m3d).*exp(rp3d).^(1-theta) ...
    - (1-sm)^(sm-1)*sm^(-sm)*omega^(1-sm)*exp(l3d).^(psi*(1-sm)).*exp(rad3d).^(gamma*(1-sm)).*exp(-a3d).*exp(rad3d+m3d).*exp(rp3d).^(-theta);
rPi = reshape(rPi3d,[Ssize 1]);

for ii = 1:NSectors
    menucost(ii).menucost = reshape(omega2*K(ii)*exp(rad3d).^gamma,[Ssize 1]);
end

for ii = 1:NSectors
    menucost2(ii).menucost2 = reshape(omega2*K2(ii)*exp(rad3d).^gamma,[Ssize 1]);
end

clear a3d rp3d rad3d rPi3d l3d m3d

% Calculate the ratio of marginal utility
%**************************************************************
% The (i,j)th element of RMU is the ratio of marginal utility in 
% state j of period t+1 to the marginal utility in state i of
% period t.

RMU = ((1./exp(rad))*(exp(rad)')).^(-gamma);

% Initialize ErV matrix (Expected Value next period)
%**************************************************************

for ii = 1:NSectors
    rV(ii).rV = 1.5*ones(Ssize, 1)*max(0,mean(rPi)/(1-beta));
end

rPi3d = reshape(rPi,[agridsize rpgridsize radgridsize]);
tolV = 0.005*rPi3d(floor(agridsize/2),floor(rpgridsize/2),floor(radgridsize/2))/(1-beta);
clear rPi3d
%tolV = 0.03;

% Initialize stationary distribution Q
%**************************************************************

for ii = 1:NSectors
    Q(ii).Q = ones(Ssize,1)/Ssize;
end

tolQ = Q(1).Q(1)/10;


% Solve for the Equilibrium
%
% Call routines that solve the model
%
%**************************************************************

[G,rV,F,F2,Q] = EqSolverGeNCalvoPlus(rPi,menucost,menucost2,RMU,alphaCalvo,...
    beta,theta,a,rp,rad,Proba,ProbNgr,rV,Q,G,SectorWeights,tolV,tolQ,MaxItOnG,0);

GError = CalcGErrorMultiSectorCalvoPlus(Q,F,F2,G,alphaCalvo,a,rp,rad,theta,...
    Proba,ProbNgr,SectorWeights);

PCStats = RigidityStatsMultiSectorCalvoPlus(Q,F,F2,alphaCalvo,...
    SectorWeights,a,rp,rad);


fprintf('\n')
fprintf('GeN CalvoPlus\n\n')
fprintf('theta:     %5.5f\n',theta)
fprintf('psi:       %5.5f\n',psi)
fprintf('gamma:     %5.5f\n',gamma)
fprintf('sm:        %5.5f\n',sm)
fprintf('mu:        %5.5f\n',mu)
fprintf('sigma_eta: %5.5f\n',sigma_eta)
fprintf('FlexSSC:   %5.5f\n',exp(FlexSSC))

fprintf('K(i)/FlexSSY:  ')
for ii = 1:NSectors
    fprintf('   %5.4f ',K(ii)/exp(FlexSSY))
end
fprintf('\n')

fprintf('K2(i)/FlexSSY: ')
for ii = 1:NSectors
    fprintf('   %5.4f ',K2(ii)/exp(FlexSSY))
end
fprintf('\n')

fprintf('1-alphaCalvo:  ')
for ii = 1:NSectors
    fprintf('   %5.4f ',1-alphaCalvo(ii))
end
fprintf('\n')

fprintf('rho:           ')
for ii = 1:NSectors
    fprintf('   %5.4f ',rho(ii))
end
fprintf('\n')

fprintf('sigma_eps:     ')
for ii = 1:NSectors
    fprintf('   %5.4f ',sigma_eps(ii))
end
fprintf('\n')

fprintf('Sector Weights:')
for ii = 1:NSectors
    fprintf('   %5.4f ',SectorWeights(ii))
end
fprintf('\n')

fprintf('Overall: \n')
fprintf('Frequency of Price Change:\n')
for ii = 1:NSectors
    fprintf('   %5.4f ',PCStats.freq(ii))
end
fprintf('    ||   %5.4f \n',PCStats.avfreq)
fprintf('Frac Up:\n')
for ii = 1:NSectors
    fprintf('   %5.4f ',PCStats.fracup(ii))
end
fprintf('    ||   %5.4f \n',PCStats.avfracup)
fprintf('Size of Price Changes:\n')

for ii = 1:NSectors
    fprintf('   %5.4f ',PCStats.wmed(ii))
end
fprintf('    ||   %5.4f \n',PCStats.avwmed)
fprintf('Size of Price Increases:\n')


for ii = 1:NSectors
    fprintf('   %5.4f ',PCStats.interq(ii))
end
fprintf('    ||   %5.4f \n',PCStats.interq)
fprintf('Size of Price Decreases:\n')

for ii = 1:NSectors
    fprintf('   %5.4f ',PCStats.kur(ii))
end
fprintf('    ||   %5.4f \n',PCStats.avkur)
fprintf('\n')

fprintf('Fraction of Price Changes in Low Cost State:\n')
for ii = 1:NSectors
    fprintf('   %5.4f ',(1-alphaCalvo(ii))*PCStats.freq2(ii)/PCStats.freq(ii))
end

 
%/************ COMPUTE V(C)
Qrad = zeros(radgridsize,1);
for ii = 1:NSectors
    Qtemp = reshape(Q(ii).Q,[agridsize*rpgridsize radgridsize]);
    Qrad = Qrad + SectorWeights(ii)*sum(Qtemp)';
end

Erad = rad'*Qrad;
VARrad = Qrad'*((rad-Erad).^2);

% Print Results
%**************************************************************************

fprintf('St.Dev of output = %5.5f (x10^-2)\n',(VARrad^(1/2))*100)
fprintf('Variance of output = %5.9f (x10^-4)\n\n',VARrad*10000)
 


%COMPUTE IRF
NSim = 200;  %%rather than 25000
burnin = 200;  %%rather than 20
NPeriods = NSim + burnin;
nhh = 2.2; % bandwidth of kernel smoother (number of rad points/2)
radincsmooth = 10^(-6);
radgridsize = size(rad,1);

radinc = rad(2)-rad(1);
hh = nhh*radinc;
AddN = hh/radinc - mod(hh/radinc,1);
radLong = rad;
GplusError = G + GError;
GLong = GplusError;
for i = 1:AddN
    radLong = [rad(1)-i*radinc; radLong; rad(end)+i*radinc];
    GLong = [GplusError(1) - GplusError(1+i) + GplusError(1); ...
        GLong; GplusError(end) - GplusError(end-i) + GplusError(end)];
end

Nsmooth = (rad(end)-rad(1))/radincsmooth + 1;
radSmooth = (rad(1):radincsmooth:rad(end))';
GSmooth = KernelSmoother(hh,radLong,GLong,radSmooth);

% Put GSmooth on radSmooth grid
%********************************************************
 
radSmoothinc = radSmooth(2) - radSmooth(1);
GSmooth_mod = mod(GSmooth,radSmoothinc);
GSmooth_mod_up = (GSmooth_mod > radSmoothinc/2);
GSmooth = GSmooth + GSmooth_mod_up.*(radSmoothinc-GSmooth_mod) ...
    - (1-GSmooth_mod_up).*GSmooth_mod;

% Simulate series for S
%********************************************************

%%Herve approach: do not simulate an idiosyncratic shock in the alternative

dS_alt = mu + 0*randn(NPeriods,1);
dS_alt(burnin+3)=mu+0.0028;         %% Shock in period 3  

% Put dS on the radSmooth grid
dS_mod = mod(dS_alt,radSmoothinc);
dS_mod_up = (dS_mod > radSmoothinc/2);
dS_alt = dS_alt + dS_mod_up.*(radSmoothinc-dS_mod) ...
    - (1-dS_mod_up).*dS_mod;

S_alt = zeros(NPeriods+1,1);
for ii = 1:NPeriods
    S_alt(ii+1,1) = S_alt(ii,1) + dS_alt(ii,1);
end
S_alt = S_alt(2:end,1);

% Calculate the steady state of S/P
%********************************************************

S_alt = S_alt + radSmooth(floor(Nsmooth/2),1);

% Simulate Economy
%*********************************************************

SPm_alt = zeros(NPeriods,1);
SP_alt = zeros(NPeriods,1);
P_alt = zeros(NPeriods+1,1);
Pi_alt = zeros(NPeriods,1);

for ii = 1:NPeriods
    SPm_alt(ii,1) = S_alt(ii,1) - P_alt(ii,1);
    if SPm_alt(ii,1) < radSmooth(1,1)
        SPm_alt(ii,1) = radSmooth(1,1);
    elseif SPm_alt(ii,1) > radSmooth(end,1)
        SPm_alt(ii,1) = radSmooth(end,1);
    end
    %int32(SPm(ii,1)*10^6)
    %min(abs(int32(SPm(ii,1)*10^6)*int32(ones(Nsmooth,1))-int32(radSmooth*10^6)))
    [dummy,IndInf] = ismember(int32(SPm_alt(ii,1)*10^6),int32(radSmooth*10^6));
    clear dummy
  
    %IndInf = match(int32(SPm(ii,1)*10^6),int32(radSmooth*10^6));
    P_alt(ii+1,1) = P_alt(ii,1) + GSmooth(IndInf,1);
    Pi_alt(ii,1) = P_alt(ii+1,1) - P_alt(ii,1);
    SP_alt(ii,1) = S_alt(ii,1) - P_alt(ii+1,1);
end

S_alt = S_alt(1:end,1);
SPm_alt = SPm_alt(1:end,1);
SP_alt = SP_alt(1:end,1);
P_alt = P_alt(1:end,1);
Pi_alt = Pi_alt(1:end,1);

IRF=SP_alt(burnin:burnin+NSim)-SP_alt(end)

figure; plot(IRF)


  freq=PCStats.freq;
  fracup=PCStats.avfracup;
  med=PCStats.avwmed;
  interq=PCStats.avinterq;
  kur=PCStats.avkur;
  absq1=PCStats.w25(1);
  absq2=PCStats.wmed(1);
  absq3=PCStats.w75(1);
  share_Calvo=(1-alphaCalvo(1))*PCStats.freq2(1)/PCStats.freq(1);
  mu_p=mu_c*3/4;
  MC_paid=freq*(1-share_Calvo)*mu_p*100;
  moments=[freq  fracup med interq kur absq1 absq2 absq3 share_Calvo mu_p MC_paid];
    VC=VARrad*100;
    
end
 
 

